Question

question
solve for ( x ) and graph the solution on the number line below.
( 19 < -4x - 9 ) or ( -4x - 9 < -13 )

answer attempt 1 out of 2

inequality notation:

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, arrows left and right, text click and drag to plot line.

Explanation:

Step1: Solve \(19 < -4x - 9\)

Add 9 to both sides: \(19 + 9 < -4x - 9 + 9\)
\(28 < -4x\)
Divide both sides by -4 (reverse inequality): \(\frac{28}{-4} > \frac{-4x}{-4}\)
\(-7 > x\) or \(x < -7\)

Step2: Solve \(-4x - 9 < -13\)

Add 9 to both sides: \(-4x - 9 + 9 < -13 + 9\)
\(-4x < -4\)
Divide both sides by -4 (reverse inequality): \(\frac{-4x}{-4} > \frac{-4}{-4}\)
\(x > 1\)

Step3: Combine solutions

Since it's "or", the solution is \(x < -7\) or \(x > 1\)

Answer:

Inequality Notation: \(x < -7\) or \(x > 1\)
(For the number line: Plot an open circle at -7 and shade to the left, plot an open circle at 1 and shade to the right.)